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How Compressible Are Innovation Processes?
KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering. Sharif Univ Technol, Elect Engn Dept, Tehran 11155, Iran.
Sharif Univ Technol, Elect Engn Dept, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
Sharif Univ Technol, Elect Engn Dept, Tehran 11155, Iran.;Sharif Univ Technol, Adv Commun Res Inst, Tehran 11155, Iran..
2018 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 64, no 7, p. 4843-4871Article in journal (Refereed) Published
Abstract [en]

The sparsity and compressibility of finitedimensional signals are of great interest in fields, such as compressed sensing. The notion of compressibility is also extended to infinite sequences of independent identically distributed or ergodic random variables based on the observed error in their nonlinear k-term approximation. In this paper, we use the entropy measure to study the compressibility of continuous-domain innovation processes (alternatively known as white noise). Specifically, we define such a measure as the entropy limit of the doubly quantized (time and amplitude) process. This provides a tool to compare the compressibility of various innovation processes. It also allows us to identify an analogue of the concept of "entropy dimension" which was originally defined by Renyi for random variables. Particular attention is given to stable and impulsive Poisson innovation processes. Here, our results recognize Poisson innovations as the more compressible ones with an entropy measure far below that of stable innovations. While this result departs from the previous knowledge regarding the compressibility of impulsive Poisson laws compared with continuous fat-tailed distributions, our entropy measure ranks alpha-stable innovations according to their tail.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018. Vol. 64, no 7, p. 4843-4871
Keywords [en]
Compressibility, entropy, impulsive Poisson process, stable innovation, white Levy noise
National Category
Telecommunications
Identifiers
URN: urn:nbn:se:kth:diva-240220DOI: 10.1109/TIT.2018.2822660ISI: 000435979500010Scopus ID: 2-s2.0-85048999645OAI: oai:DiVA.org:kth-240220DiVA, id: diva2:1271208
Note

QC 20181217

Available from: 2018-12-17 Created: 2018-12-17 Last updated: 2018-12-17Bibliographically approved

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